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Dieses Open-Access-Buch behandelt für eine breite Klasse zweidimensionaler Variationsprobleme eine Existenz- und Regularitätstheorie, die der Lösung von Randwertproblemen partieller Differentialgleichungssysteme dient. Dabei werden bekannte Ergebnisse gründlich untersucht und umfassend aufgearbeitet. Teilweise wird eine geeignete Anpassung der Voraussetzungen einiger Resultate vorgenommen. Speziell wird die Theorie auf das Plateausche Problem für Flächen vorgeschriebener mittlerer Krümmung im ℝ³ angewendet. Der Autor Andreas Künnemann ist wissenschaftlicher Mitarbeiter am Institut für Mathematik der Brandenburgischen Technischen Universität Cottbus-Senftenberg. Seine Forschungsinteressen sind Lösbarkeits- und Regularitätsfragen partieller Differentialgleichungen sowie die damit verbundenen Theorien der Funktionalanalysis, Variationsrechnung und Funktionentheorie.

Mathematical analysis. --- Differential equations. --- Analysis. --- Differential Equations. --- 517.91 Differential equations --- Differential equations --- 517.1 Mathematical analysis --- Mathematical analysis

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Mathematical analysis --- Mathematical analysis. --- Advanced calculus --- Analysis (Mathematics) --- 517.1 Mathematical analysis --- Algebra

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Mathematics --- Mathematical analysis --- Mathematical physics --- Analyse mathématique --- 517.1 Mathematical analysis --- Mathematical analysis. --- Advanced calculus --- Analysis (Mathematics) --- Algebra

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Inverse problems are usually nonlinear and are separated into one-dimensional and multidimensional problems, depending on whether the sought function (or functions) is a function of one variable or of many. Multidimensionality of inverse problems has particular value at present, because practice shows that many investigating processes are described by an equation, of which the co-efficient essentially depends on many variables. This monograph is devoted to statements of multidimensional inverse problems, in particular to methods of their investigation. Questions of the uniqueness of solution, solvability and stability are studied. Methods to construct a solution are given and, in certain cases, inversion formulas are given as well. Concrete applications of the theory developed here are also given. Where possible, the author has stopped to consider the method of investigation of the problems, thereby sometimes losing generality and quantity of the problems, which can be examined by such a method. The book should be of interet to researchers in the field of applied mathematics, geophysics and mathematical biology.

Inverse problems (Differential equations) --- Differential equations. --- 517.91 Differential equations --- Differential equations --- Differential Equations. --- Ill-Posed Problems. --- Inverse Problems.

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Differential equations --- Equations différentielles --- Periodicals. --- Périodiques --- Differential equations. --- Mathematical Sciences --- Applied Mathematics --- Ejournals --- UML. --- differential equations --- Equations, Differential --- Bessel functions --- Calculus --- 517.91 Differential equations --- Mathematics